No, it’s not likely that herbicide applications lead to cyanobacteria blooms. Herbicides work by targeting specific aspects of a plant’s internal cellular processes. This allows them to kill one kind of plant, but not another. Freshwater algae and cyanobacteria do share many cellular processes with terrestrial plants. A number of recent papers indicate that both algae and cyanobacteria are sensitive to many different herbicides (for example, Gomes and Juneau 2017, Singh et al. 2016, Hernadez-Garcia and Martinez-Jeronimo 2020). Just how much they are affected depends on the herbicide, when/how it is applied, and environmental conditions at the time of application. Applicators must take this into account and apply herbicides that target the nuisance plant primarily and limit effects on non-target species. Applied properly, herbicides should not change phytoplankton community structure to favor cyanobacteria.
Cyanobacteria grow in aquatic environments with many other inhabitants. Competition for light, nutrients, and space to grow has led many species to develop abilities that allow them to access what they need better than others can. When you look at the phytoplankton communities in lakes affected by cyanobacteria blooms, they are not conspicuous because of the lack of other algae like diatoms and green algae. On Carmi, St. Albans, and Missisquoi, there are major spring diatom blooms and masses of green algae in summer along the shorelines. They also support large communities of aquatic plants. This is true even during persistent bloom events and over many years despite persistent blooms. Cyanobacteria dominance at a certain time of the year is more likely connected to other characteristics like temperature and nutrients than to the use of herbicides. You can read more about cyanobacteria from retired aquatic biologist Angela Shambaugh in her FOVLAP website article here: “Cyanobacteria”.